A straight, solid line connects plotted points E and F on a coordinate plane. The line slopes downward from left to right. Point E is left parenthesis negative 6 comma 1 right parenthesis. Point F is left parenthesis 2 comma negative 5 right parenthesis.

Question

How would you set up the distance formula to find the distance between points E and F .

(1 point)
Responses

d=((−2)+6)2+(5+1)2−−−−−−−−−−−−−−−−−−√
d is equal to square root of open paren negative 2 plus 6 close paren squared plus open paren 5 plus 1 close paren squared end root

d=(6−2)2+(1−5)2−−−−−−−−−−−−−−−√
d is equal to square root of open paren 6 minus 2 close paren squared plus open paren 1 minus 5 close paren squared end root

d=(−6−2)2+(1−(−5))2−−−−−−−−−−−−−−−−−−−√
d is equal to square root of open paren negative 6 minus 2 close paren squared plus open paren 1 minus negative 5 close paren squared end root

d=(2−6)2+(5−1)2−−−−−−−−−−−−−−−√

Answer 1

To find the distance between points E and F using the distance formula, we first recall the points: \(E(-6, 1)\) and \(F(2, -5)\).

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

With \(E\) as \((x_1, y_1)\) = \((-6, 1)\) and \(F\) as \((x_2, y_2)\) = \((2, -5)\), we substitute these values into the formula:

\[ d = \sqrt{(2 - (-6))^2 + (-5 - 1)^2} \] which simplifies to: \[ d = \sqrt{(2 + 6)^2 + (-5 - 1)^2} \] or: \[ d = \sqrt{(8)^2 + (-6)^2} \]

Now, let's look at the responses provided. The correct setup using the distance formula is:

\[ d = \sqrt{(2 - (-6))^2 + (-5 - 1)^2} \]

So the correct choice among the options is:

d = \sqrt{(−6−2)^2 + (1−(−5))^2} (This is incorrectly expressed, but if intended to show the operation for finding distance could resemble a similar structure; however, the accurate representation is given above).

Therefore, the closest correct answer, representing the step of finding distance in appropriate terms, is:

Final correct setup: \[ d = \sqrt{(2 + 6)^2 + (-5 - 1)^2} \]

However, in the options given, ensure to select the setup best representing the calculation.

Answer 2

DaQuan marks two points on the coordinate plane. One point is L(4,2) and the other point is M(7,6). What is the correct way for DaQuan to set up the distance formula?(1 point)
Responses

d=(2−4)2+(6−7)2−−−−−−−−−−−−−−−√
d is equal to square root of open paren 2 minus 4 close paren squared plus open paren 6 minus 7 close paren squared end root

d=(2−7)2+(4−6)2−−−−−−−−−−−−−−−√
d is equal to square root of open paren 2 minus 7 close paren squared plus open paren 4 minus 6 close paren squared end root

d=(4−7)2+(2−6)2−−−−−−−−−−−−−−−√
d is equal to square root of open paren 4 minus 7 close paren squared plus open paren 2 minus 6 close paren squared end root

d=(6−7)2+(2−4)2−−−−−−−−−−−−−−−√

Answer 3

To find the distance between points \(L(4, 2)\) and \(M(7, 6)\) using the distance formula, we can use the formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Where \((x_1, y_1)\) represents point \(L\) and \((x_2, y_2)\) represents point \(M\). Here, \(L(4, 2)\) means \(x_1 = 4\) and \(y_1 = 2\), and \(M(7, 6)\) means \(x_2 = 7\) and \(y_2 = 6\).

Substituting these coordinates into the distance formula, we have:

\[ d = \sqrt{(7 - 4)^2 + (6 - 2)^2} \]

This simplifies to:

\[ d = \sqrt{(3)^2 + (4)^2} \] or, equivalently:

\[ d = \sqrt{(4 - 7)^2 + (2 - 6)^2} \]

Now, let's review the options provided:

1. \(d = \sqrt{(2 - 4)^2 + (6 - 7)^2}\)
2. \(d = \sqrt{(2 - 7)^2 + (4 - 6)^2}\)
3. \(d = \sqrt{(4 - 7)^2 + (2 - 6)^2}\)
4. \(d = \sqrt{(6 - 7)^2 + (2 - 4)^2}\)

The correct setup that matches our derived expression is:

d = \sqrt{(4 - 7)^2 + (2 - 6)^2}

Thus, the correct choice is:

3. \(d = \sqrt{(4 - 7)^2 + (2 - 6)^2}\).

Answer 4

Parallelogram upper A upper B upper C upper D is graphed on a coordinate plane. The x-axis ranges from negative 6 to 6 in increments of 1. The y-axis ranges from negative 6 to 6 in increments of 1.
Use the given coordinates to compute the perimeter of the parallelogram.

(1 point)
Responses

13.3 units
13.3 units

28 units
28 units

25.2 units
25.2 units

26.6 units

Answer 5

To compute the perimeter of the parallelogram \(ABCD\), we need the coordinates of points \(A\), \(B\), \(C\), and \(D\). Since the specific coordinates are not provided in your question, I will guide you through the general steps needed to calculate the perimeter.

1. Identify the Coordinates: Write down the coordinates of all four vertices \(A\), \(B\), \(C\), and \(D\).

2. Calculate the Length of One Side: Use the distance formula to find the lengths of the sides. The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

   \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

   Calculate the length of side \(AB\) using its coordinates \(A(x_1, y_1)\) and \(B(x_2, y_2)\).

3. Calculate the Length of the Adjacent Side: Calculate the length of side \(BC\) using points \(B\) and \(C\).

4. Calculate the Perimeter: Since a parallelogram has two pairs of equal sides, the perimeter \(P\) can be calculated using:

   \[ P = 2 \times (AB + BC) \]

Example Calculation

If the coordinates were as follows:

• \(A(-2, 2)\)
• \(B(2, 2)\)
• \(C(4, -2)\)
• \(D(0, -2)\)

1. Calculate the lengths:

   • Length of \(AB\): \[ d = \sqrt{(2 - (-2))^2 + (2 - 2)^2} = \sqrt{(4)^2 + (0)^2} = 4 \]

   • Length of \(BC\): \[ d = \sqrt{(4 - 2)^2 + (-2 - 2)^2} = \sqrt{(2)^2 + (-4)^2} = \sqrt{4 + 16} = \sqrt{20} \approx 4.47 \]

2. Calculate the perimeter: \[ P = 2 \times (AB + BC) = 2 \times (4 + 4.47) \approx 2 \times 8.47 \approx 16.94 \text{ units} \]

Conclusion

Please provide the coordinates of the points \(A\), \(B\), \(C\), and \(D\), or check your calculations if you have completed them with the specific values. With the coordinates, you can follow the above steps to confirm the perimeter.

Based on provided available options (13.3, 28, 25.2, 26.6 units), once you compute, see which of these best matches your calculated perimeter.